Improved Approximations for Guarding 1.5-Dimensional Terrains
نویسندگان
چکیده
منابع مشابه
A 4-Approximation Algorithm for Guarding 1.5-Dimensional Terrains
In the 1.5-dimensional terrain guarding problem we are given as input an x-monotone chain (the terrain) and asked for the minimum set of guards (points on the terrain) such that every point on the terrain is seen by at least one guard. It has recently been shown that the 1.5-dimensional terrain guarding problem is approximable to within a constant factor [3,7], though no attempt has been made t...
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Let P be a polygon with n vertices. We say that two points of P see each other if the line segment connecting them lies inside (the closure of) P . In this paper we present efficient approximation algorithms for finding the smallest set G of points of P so that each point of P is seen by at least one point of G, and the points of G are constrained to be belong to the set of vertices of an arbit...
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A 1.5-dimensional terrain T with n vertices is an xmonotone polygonal chain in the plane. A point guard p on T guards a point q of T if the line segment connecting p to q lies on or above T ; p is a vertex guard if it is a vertex of T . In the Optimal Terrain Guarding (OTG) problem on T , the objective is to guard the vertices of T by the minimum number of vertex guards. King and Krohn [9] show...
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We prove that [n/2J vertex guards are always sufficient and sometimes necessary to guard the surface of an n-vertex polyhedral terrain. We also show that l(4n 4)/13J edge guards are sometimes necessary to guard the surface of an n-vertex polyhedral terrain. The upper bound on the number of edge guards is ln/3J (Everett and Rivera-Campo, 1994). Since both upper bounds are based on the four color...
متن کاملGuarding Terrains via Local Search
We obtain a polynomial time approximation scheme for the 1.5D terrain guarding problem, improving upon several recent constant factor approximations. Our algorithm is a local search algorithm inspired by the recent results of Chan and Har-Peled [3] and Mustafa and Ray [18]. Our key contribution is to show the existence of a planar graph that appropriately relates the local and global optimum.
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ژورنال
عنوان ژورنال: Algorithmica
سال: 2009
ISSN: 0178-4617,1432-0541
DOI: 10.1007/s00453-009-9358-4